The Dual of a Parabolic Subgroup and a Degenerate Principal Series of Sp(n, C)

Introduction. Although the work of Harish-Chandra yields, the Plancherel formula for complex semi-simple Lie groups, the (unitary) representation theory of such groups remains incomplete in the sense that the dual object has not yet been completely determined, except in the case of SL(2, C)and possibly SL (n, C) for n> 2. The suggested constituents of the dual object fall into various series of representations which one refers to as pritncipal series or complementary series.